Saturday, August 27, 2011

An interesting method of multiplication

In this article I will try to show an interesting way to multiply two numbers. This method is called the Russian Peasant Multiplication, also known as Russian Multiplication. Multiplication of two numbers as, most of us would normally know of is pretty simple and straightforward.

The normal or most commonly used method [without using a calculator, of course] may best be demonstrated with the help of an example.

Let the two numbers be 16 and 13. We would then write down the two numbers so that, one is below the other making sure that, the digits in the units place are aligned vertically as shown below.

16x 13160+ 48208

This method works simply because of the Distributive Law which, when applied to multiplication states that,

a×b+a×c=a(b+c)

If, the two numbers are substituted into this law such that, a = 16, b = 10 and c = 3 we get:

16×10+16×3=16(10+3)

Now, let us move onto the Russian method. In this method, the two numbers are written in the top row of two columns. One is halved ignoring the remainder and the other is doubled moving down the column, until the halved column reaches 1. Then, all the rows with an even number in the halving column are crossed out. The remaining numbers in the doubled column are then added up which, gives the product of the two numbers.

Let us see and example. This time we will pick numbers 98 and 82.

halving

doubling

98

82

49

164

24

328

12

658

6

1316

3

2624

1

5248

Now adding up all the remaining numbers in the doubling column gives:

164 + 2624 + 5248 = 8036

However cumbersome, this is an interesting way to multiply because, it leaves one wondering if, there could be other ways to do multiplication.